Error inequalities for a quadrature formula and applications

Abstract

An optimal two-point quadrature formula of open type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known two-point Gauss quadrature formula. Various error inequalities for this formula are established. Applications in numerical integration are given.

Several error inequalities for a quadrature formula with a parameter and applications

“…For example see [1][2][3] where the midpoint and trapezoid quadrature rules are considered. In [4], N. Ujević obtained the following optimal two-point quadrature formula in the sense that it has a minimal error bound. 1 2 ].…”

A note on some Ostrowski-like type inequalities

“…The midpoint and the trapezoid rules are typical quadrature rules and their error estimates are studied in [1][2][3][4][5]. Recently, Huy and Ngô introduced a new type of quadrature formula in [6,7] and they also establish some new Ostrowski-like type inequalities.…”

Pure and Applied Mathematics

“…Moreover, it is worth-mentioning that the family of quadrature formulae thus obtained hereafter is a generalization of that presented in [99].…”

“…In [28,34,81], the quadrature problem, in particular, the investigation of error In this section, we present an approach similar to that of Ujevic's [99] to present some improvements and generalizations in this context.…”

“…as de…ned in [99], where x; y 2 [a + h (b a) ; b h (b a)] ; h 2 0; 1 2 ; x < y and ; 1 ; ; 1 ; ; 1 2 R are parameters which are required to be determined.…”